The uniformly bounded energy, Morawertz's estimate, energy and pointwise decays are obtained naturally in the program to prove linear and nonlinear stability of black hole spacetimes and the related problems (see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}). The method of \(r^p\) -theory of Dafermos and Rodnianski [11]} is an essential tool of the proof in a lot of work later.
